# Complex number algebra question

• Mar 11th 2013, 11:21 PM
Vishak
Complex number algebra question
Hi, can someone please verify my answers to this question. Thanks heaps!!

Find all complex numbers w and z satisfying:

1/w + 1/z = 1/wz and 2wz - z^2 -1 = 0

- I got the answers z = 1/3 +(or)- (√2 / 3) i and w = 2/3 + (or) - (√2 / 3)i
• Mar 11th 2013, 11:50 PM
ibdutt
Re: Complex number algebra question
You are absolutely right.
• Mar 12th 2013, 09:36 AM
smatik
Re: Complex number algebra question
Yea correct.
• Mar 13th 2013, 03:41 AM
algerber
Re: Complex number algebra question
Multiply both sides of $\frac{1}{z}+ \frac{1}{w}= \frac{1}{wz}$ by wz to get w+ z= 1. Then w= 1- z so the second equation becomes $2wz - z^2 -1= 2(1- z)z- z^2- 1= 2z- 2z^2- z^2- 1= -3z^2+ 2z- 1 = 0$ which the same as $3z^2- 2z+ 1= 0$. Use the quadratic formula, or complete the square, to solve that for z